Electrical Engineering ⇒ Topic : Inductance element
In a pure inductive circuit Figure (1), we have
Figure (a) Pure inductive circuit.
Taking Laplace transform of Eq. (1), we can write
V(s) = L[s I(s) - i(0-) ]
or sL I(s) = V(s) + L i(0-) ............. (2)
The circuit shown in Figure (a) is redrawn in Figure (1) (s-domain) using Eq. (2).
Figure (b) Circuit of Figure (a) in s-domain.
In Figure (b), the direction of initial current i(0-) is taken the same as that of i(t). If the initial current is taken in the direction opposite to that of i(t), Eq. (2) becomes
sL I(s) = V(s) - L i(0-) .........(3)
and the circuit in Figure (b) becomes as shown in Figure (C).
Figure (C) Circuit of Figure (B) redrawn with direction of initial current opposite to that of i(t).
From Eq. (2), we can write
Figure (D) Equivalent circuit of a pure inductive element in s-domain
The equivalent circuit in Laplace domain is shown in Figure (D).
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